Queueing Theory - M1 - 6EC

1) Introduction

Waiting is inherently related to many situations that we encounter in practice. Some examples of such practical situations are production systems, transportation and stocking systems, communication systems, and health care systems. Queuing models are particularly useful for the design of these systems in terms of layout, capacities and control. In this course, we focus on the mathematical analysis of a number of elementary queueing models. Specifically, as waiting primarily occurs due to randomness in the arrival and service processes of customers, queueing theory is embedded in the field of applied probability. We mainly pay attention to methods for the analysis of queueing models, but also to its applications. 

2) Aim of the course

In this course, you will learn the theory of queueing models with one queue. The main focus will be on the methods for solving queueing models, whereas model formulation and insights will also be addressed. More specifically, the following subjects will be treated:

  • Fundamental queueing relations (Little's law, PASTA property)

  • Markovian queues (M/M/1 queue, M/M/c queue, M/E_r/1 queue)

  • M/G/1 queue and G/M/1 queue

  • Mean value technique

  • Priority queues

  • Variations of the M/G/1 queue

  • Insensitive queues (M/G/c/c queue and M/G/infinity queue)

3) Prerequisites
Basic knowledge of probability at the level:

  • S.M. Ross, Introduction to probability models, 9th edition, Academic Press, 2007 (chapters 1-3).

4) Rules about Homework / Exam

There are two homework assignments and a final written exam.

The final grade (FG) is determined by the grade of the written exam (E) and both homework sets (HW1 and HW2) as follows, before the appropriate rounding:

FG = (0.8*E + 0.1*HW1 + 0.1*HW2)*1{E>=5.0} + E*1{E<5.0},

where 1{.} refers to the indicator function. In words, in case the exam grade is at least 5.0, it counts for 80%, while the two homework sets count for 10% each. If not, the final grade is given by the exam grade itself, which means the course has not been passed.

The homework cannot be retaken, but there is a resit opportunity for the exam (the grade of which is referred to as RE). In case a resit is required the final grade after resit (FGR) is determined as follows:

FGR = Max{0.8*RE + 0.1*HW1+ 0.1*HW2, RE}*1{RE>=5.0} + RE*1{RE<5.0}.

In words, the same weights as well as the requirement of at least a grade of 5.0 still apply, but the homework now only contributed beneficially to the final grade.

5) Literature

The course material consists of the lecture notes on Queueing Theory, written by Ivo Adan and Jacques Resing of the TUE. It contains all material for the course, as well as many relevant exercises, and most answers/solutions. 

The lecture notes are freely available as a pdf file at http://www.win.tue.nl/~iadan/queueing.pdf.